///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtx_rotate_vector
/// @file glm/gtx/rotate_vector.inl
/// @date 2006-11-02 / 2011-06-07
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm {
    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec3<T, P>
    slerp
    (
            tvec3<T, P>
    const & x,
    tvec3<T, P> const &y,
            T
    const & a
    ) {
    // get cosine of angle between vectors (-1 -> 1)
    T CosAlpha = dot(x, y);
    // get angle (0 -> pi)
    T Alpha = acos(CosAlpha);
    // get sine of angle between vectors (0 -> 1)
    T SinAlpha = sin(Alpha);
    // this breaks down when SinAlpha = 0, i.e. Alpha = 0 or pi
    T t1 = sin((static_cast<T>(1) - a) * Alpha) / SinAlpha;
    T t2 = sin(a * Alpha) / SinAlpha;

    // interpolate src vectors
    return
    x *t1
    +
    y *t2;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec2<T, P>
rotate
(
        tvec2<T, P>
const & v,
T const &angle
)
{
tvec2<T, P> Result;
T const Cos(cos(angle));
T const Sin(sin(angle));

Result.
x = v.x * Cos - v.y * Sin;
Result.
y = v.x * Sin + v.y * Cos;
return
Result;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P>
rotate
(
        tvec3<T, P>
const & v,
T const &angle,
        tvec3<T, P>
const & normal
)
{
return
tmat3x3<T, P>(glm::rotate(angle, normal)
) *
v;
}
/*
template <typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P> rotateGTX(
    const tvec3<T, P>& x,
    T angle,
    const tvec3<T, P>& normal)
{
    const T Cos = cos(radians(angle));
    const T Sin = sin(radians(angle));
    return x * Cos + ((x * normal) * (T(1) - Cos)) * normal + cross(x, normal) * Sin;
}
*/
template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec4<T, P>
rotate
(
        tvec4<T, P>
const & v,
T const &angle,
        tvec3<T, P>
const & normal
)
{
return
rotate(angle, normal
) *
v;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P>
rotateX
(
        tvec3<T, P>
const & v,
T const &angle
)
{
tvec3<T, P> Result(v);
T const Cos(cos(angle));
T const Sin(sin(angle));

Result.
y = v.y * Cos - v.z * Sin;
Result.
z = v.y * Sin + v.z * Cos;
return
Result;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P>
rotateY
(
        tvec3<T, P>
const & v,
T const &angle
)
{
tvec3<T, P> Result = v;
T const Cos(cos(angle));
T const Sin(sin(angle));

Result.
x = v.x * Cos + v.z * Sin;
Result.
z = -v.x * Sin + v.z * Cos;
return
Result;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P>
rotateZ
(
        tvec3<T, P>
const & v,
T const &angle
)
{
tvec3<T, P> Result = v;
T const Cos(cos(angle));
T const Sin(sin(angle));

Result.
x = v.x * Cos - v.y * Sin;
Result.
y = v.x * Sin + v.y * Cos;
return
Result;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec4<T, P>
rotateX
(
        tvec4<T, P>
const & v,
T const &angle
)
{
tvec4<T, P> Result = v;
T const Cos(cos(angle));
T const Sin(sin(angle));

Result.
y = v.y * Cos - v.z * Sin;
Result.
z = v.y * Sin + v.z * Cos;
return
Result;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec4<T, P>
rotateY
(
        tvec4<T, P>
const & v,
T const &angle
)
{
tvec4<T, P> Result = v;
T const Cos(cos(angle));
T const Sin(sin(angle));

Result.
x = v.x * Cos + v.z * Sin;
Result.
z = -v.x * Sin + v.z * Cos;
return
Result;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tvec4<T, P>
rotateZ
(
        tvec4<T, P>
const & v,
T const &angle
)
{
tvec4<T, P> Result = v;
T const Cos(cos(angle));
T const Sin(sin(angle));

Result.
x = v.x * Cos - v.y * Sin;
Result.
y = v.x * Sin + v.y * Cos;
return
Result;
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P>
orientation
(
        tvec3<T, P>
const & Normal,
tvec3<T, P> const &Up
)
{
if(
all(equal(Normal, Up)
))
return
tmat4x4<T, P>(T(1)
);

tvec3<T, P> RotationAxis = cross(Up, Normal);
T Angle = acos(dot(Normal, Up));

return
rotate(Angle, RotationAxis
);
}
}//namespace glm
